11.8: Surveys

Difficulty Level: At Grade Created by: CK-12

Introduction

A Question of Racing

After all of this research about the Iditarod, Thomas is inspired. He wants to conduct a survey of his classmates about the Iditarod.

First, Thomas has to decide upon a question. He wants to know how many \begin{align*}7^{th}\end{align*} graders would be willing to race in the Iditarod when they are 18 years old. He knows that a good survey question will use who, what, when, where or how. He decides to use this question.

“Would you be willing to race in the Iditarod in Alaska when you are 18 years old?”

After learning about the youngest person to ever race in the Iditarod, Thomas decided to make his question very specific for age. The youngest person to ever race in the Iditarod was Dallas Seavey in 2005. He was just 18 years old. He has raced it several times since.

Now that Thomas has his question, he needs to figure out which sample he is going to use. He wants to survey \begin{align*}7^{th}\end{align*} graders like himself. Thomas only wants to survey \begin{align*}7^{th}\end{align*} graders so that his sample will be accurate.

Thomas knows of two great places to survey students. He has narrowed it down to either the \begin{align*}7^{th}\end{align*} grade adventure program or the \begin{align*}7^{th}\end{align*} grade lunch in the cafeteria. His concern about the adventure program is that not all of the students are enrolled in it. In the cafeteria, every student in the \begin{align*}7^{th}\end{align*} grade attends lunch at the same time.

Thomas is puzzled. He begins to think carefully about which group is the best survey.

What do you think? Do you have an idea why one sample group might be better versus another? This lesson is all about surveys. You will learn all about them and why one sample creates a more accurate report. By the end of this lesson, you will know how to help Thomas with his dilemma.

What You Will Learn

In this lesson you will learn to complete the following:

• Collect and organize real-world survey data.
• Choose the most effective data displays for a specified purpose.
• Identify potentially biased samples and survey questions.
• Analyze and interpret statistical survey data.

Teaching Time

I. and II. Collect, Organize and Display Real-World Survey Data

Surveys are used to collect information about a population or group of individuals. When a company would like to know if a group of people will purchase a new product, they create a survey. When a teacher would like to know if her students will participate in an after school science club, she creates a survey.

The first step in surveying a group of people is to write an unbiased question. Good survey questions are short and concise and usually begin with “Who, What, When, Where, Why, or How.”

The next step is to choose a random sample of participants. In a random sample, each member of a group has an equal chance at being asked to participate in the survey.

After the results of the survey are in, statisticians analyze the data and use it to make estimates about groups of people.

Then you can create a visual display of the data.

You have had lots of opportunities to graph data taken from surveys. In this lesson, you will learn to devise a survey question, to choose a random sample of participants, to choose an appropriate display for the survey results, and to analyze the data to make predictions about a group of individuals.

Write down the steps to conducting a survey in your notebook. There are four steps to the process.

Now let’s look at an example.

Example

Twenty-five households were asked to participate in a survey in which they were asked to approximate the number of hours they watch T.V. each day. The results of the survey are listed on the table below. Determine the most appropriate display for the given data.

\begin{align*}4 \quad 7 \quad 2 \quad 1 \quad 0 \quad 5 \quad 3 \quad 4 \quad 5 \quad 2 \quad 1 \quad 0 \quad 3 \quad 4 \quad 5 \quad 6 \quad 3 \quad 2 \quad 1 \quad 2 \quad 3 \quad 6 \quad 4 \quad 5 \quad 4\end{align*}

A frequency table and histogram will depict the most and least frequent number of hours of television watched.

Interval (Hours of Television) Tally Frequency
0 – 1 I I I I I 5
2 – 3 I I I I I I I I 8
4 – 5 I I I I I I I I I 9
6 – 7 I I I 3

Now let’s draw some conclusions based on the data and the display.

Looking at the histogram, you can see that the majority of families that participated in the survey watch between four and five hours of television each night. Five families watch between zero and one hours of television each night. Eight families watch between two and three hours of television nightly. Three of the twenty-five families watch between six and seven hours of television each night.

Example

One hundred people were asked to participate in a survey about cereal. Participants were asked to choose their favorite from a list of ten cereals. The results of the survey are listed below.

Cereal Amount
Fruit Flakes 12
Chocolate Puffs 18
Oat-O’s 9
Raisin Delight 3
Honey Crunch 17
Bran Loops 3
Oat Squares 9
Fiber Max 2
Fruities 10
Cinnamon Squares 17

Display the results on a bar graph to compare the results for each type of cereal.

III. Identify Potentially Biased Samples and Survey Questions

A population is a group about which you want information. Because it is impossible to survey an entire population, a sample or part of the population is chosen to participate in the survey. The results from the sample group are used to make estimates about the population. Larger samples lead to more reliable estimates about the population. In a random sample, each member of the population has an equal chance of being chosen to participate in the survey. Using random samples reduces the likelihood of bias.

It is important to create and conduct a survey without bias.

The first way to prevent bias is to ensure that participants are chosen randomly. For example, if surveying high school students about their favorite sport, it would be biased to take your only sample at the Friday night football game. Your survey results will be more valid and reliable if for example, you survey every fifth student that walks through the hallway.

A well written survey question is another way to prevent bias. Survey questions should be written clearly and concisely and should begin with “Who, What, When, Why, Where, or How.”

Example

You would like to conduct a survey to determine what activities middle school students like to do on the weekends. To ensure an unbiased sample, you should:

a. Go to the mall and survey every tenth person that walks by.

b. Survey middle school students at a local movie theatre.

c. Survey every fifth person leaving each of your classes.

“C” is the best answer. You should avoid taking the survey at the mall and the movies because it is likely that those participants will all say the mall or the movies as their favorite activity.

Example

You would like to know which types of dog food are most popular. You decide to wait outside three local pet food stores and interview every other person that comes out. Will your plan yield an unbiased sample?

Yes, it is best to survey participants coming out of a pet food store because you know they are there to purchase pet products. Conducting the survey at three stores will yield a larger sample which will lead to more reliable results. You may also want to consider interviewing veterinarians or people at dog parks.

Example

You survey every other person leaving a neighborhood pool. 89% of the participants support a proposal to purchase new chairs and umbrellas. Should you report that there is overwhelming support for your proposal?

While there is overwhelming support for your proposal, the sample in which you took the survey is biased. It is likely that the people who use the pool frequently will support the idea of new chairs and umbrellas. It would be wise to randomly sample other people from the neighborhood.

IV. Analyze and Interpret Statistical Survey Data

Data is analyzed after it is collected and organized on a graph. Survey results are used to make predictions about a population.

Example

Recall that twenty-five families were asked to state the number of hours they watch television each day. Use the results from the survey to answer the questions below.

Interval (Hours of Television) Tally Frequency
0 – 1 I I I I I 5
2 – 3 I I I I I I I I 8
4 – 5 I I I I I I I I I 9
6 – 7 I I I 3

What percentage of participants stated they watch between four and five hours of television per day?

Nine participants out of twenty-five stated that they watch between four and five hours of television per day. To determine the percentage, express nine out of twenty-five as a fraction. This can be converted to an equivalent fraction with a denominator of one hundred. To do so, multiply the numerator and denominator by four.

\begin{align*}& \underline{9} \times 4 = \underline{36} = 36 \% \\ & \frac{36}{100}\end{align*}

36% of the participants stated that they watch between four and five hours of television each day.

Example

Recall that one hundred people were asked to choose their favorite cereal. Use the results from the survey to answer the questions below.

What percentage of participants stated that they liked cereal with oats?

Nine participants stated they liked Oat-O’s. Nine participants stated that they liked Oat Squares. Therefore, eighteen out of the one hundred participants chose cereal with oats as their favorite. Eighteen out of one hundred is eighteen percent.

Whether you use survey data to answer questions or to draw your own conclusions, using a survey can help you to understand how people feel about a particular topic or activity.

Real Life Example Completed

A Question of Racing

Here is the original problem once again. Reread it and then read the conclusion to the problem at the end.

After all of this research about the Iditarod, Thomas is inspired. He wants to conduct a survey of his classmates about the Iditarod.

First, Thomas has to decide upon a question. He wants to know how many \begin{align*}7^{th}\end{align*} graders would be willing to race in the Iditarod when they are 18 years old. He knows that a good survey question will use who, what, when, where or how. He decides to use this question.

“Would you be willing to race in the Iditarod in Alaska when you are 18 years old?”

After learning about the youngest person to ever race in the Iditarod, Thomas decided to make his question very specific for age. The youngest person to ever race in the Iditarod was Dallas Seavey in 2005. He was just 18 years old. He has raced it several times since.

Now that Thomas has his question, he needs to figure out which sample he is going to use. He wants to survey \begin{align*}7^{th}\end{align*} graders like himself. Thomas only wants to survey \begin{align*}7^{th}\end{align*} graders so that his sample will be accurate.

Thomas knows of two great places to survey students. He has narrowed it down to either the \begin{align*}7^{th}\end{align*} grade adventure program or the \begin{align*}7^{th}\end{align*} grade lunch in the cafeteria. His concern about the adventure program is that not all of the students are enrolled in it. With the cafeteria, every student in the \begin{align*}7^{th}\end{align*} grade attends lunch at the same time.

Thomas is puzzled. He begins to think carefully about which group is the best survey.

When Thomas began to think about the two groups, he started to develop some ideas why one might be a better survey group than the other. He started with the adventure group.

-probably has heard of the Iditarod

-not everyone is registered-not an accurate sample of all of the \begin{align*}7^{th}\end{align*} grade

Then Thomas began to think about his question. Because he wants to know how many \begin{align*}7^{th}\end{align*} graders would be willing to race in the Iditarod when they are 18 years old, he needs to sample the largest group of \begin{align*}7^{th}\end{align*} graders that he can.

Because every \begin{align*}7^{th}\end{align*} grader eats lunch at the same time in the cafeteria, asking every other person in line for lunch the question will give Thomas a lot of information for his survey.

Then he call tally his results and report his findings.

Vocabulary

Here are the vocabulary words that are found in this lesson.

Survey
information gathered about people’s opinion on a particular topic or activity.
Population
a group of people
Random Sample
a sample where everyone in a group has an equal chance of answering the survey question.
Sample
the part of a population that participates in a survey.

Time to Practice

Directions: Use the information provided to answer the following questions.

One hundred people were asked to participate in a survey about travel. Participants were asked to state whether they had visited each of the cities listed below.

City Number of People Who Visited:
Waikiki 85
New York City 80
San Francisco 87
Chicago 54
Dallas 35
Orlando 38
Atlanta 50
Seattle 44
Denver 32

1. Create a bar graph of the data.

2. What percent of the people visited Waikiki?

3. What percent of the people visited Denver?

4. What percent of the people did not visit Dallas?

5. What percent of the people did not visit Chicago?

6. Which city had more people visited than any other city?

7. Which city had less people visited than any other city?

Thirty students were selected at random at Montgomery High School. Each participant was asked to state the number of textbooks they were carrying at that moment. The results of the survey are depicted below. Choose the best display to depict the data. Then use the graph you created to answer the questions below.

\begin{align*}& 0 \qquad 2 \qquad 4 \qquad 3 \qquad 1\\ & 2 \qquad 5 \qquad 0 \qquad 4 \qquad 3\\ & 2 \qquad 5 \qquad 4 \qquad 3 \qquad 2\\ & 1 \qquad 0 \qquad 0 \qquad 2 \qquad 3\\ & 5 \qquad 6 \qquad 1 \qquad 2 \qquad 4\\ & 5 \qquad 6 \qquad 3 \qquad 2 \qquad 3\end{align*}

8. Which graph is the best display of the data?

9. Create that graph here.

10. What percent of the students had the most common amount of books in their backpack?

11. What percent of the students had between four and seven books in their backpack?

12. How many students had 1 book in their backpacks?

13. How many students had 0 books in their backpacks?

14. What percent had 1 book?

15. What percent had 0 books?

Create a survey question. Decide who will be the sample population. Write a few sentences to describe who will take part in the survey and how you will administer the survey. Administer the survey, record the results on a table. Choose the most appropriate display for the data. Use these questions for guidance.

16. What is your sample population?

17. How many people are in the sample?

18. Does your question use who, what, when, where or how?

19. Is your sample biased, why or why not?

20. Are your results what you expected?

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